Length metrology apparatus and methods for suppressing phase noise-induced distance measurement errors

ABSTRACT

Length metrology apparatuses and methods are disclosed for measuring both specular and non-specular surfaces with high accuracy and precision, and with suppressed phase induced distance errors. In one embodiment, a system includes a laser source exhibiting a first and second laser outputs with optical frequencies that are modulated linearly over large frequency ranges. The system further includes calibration and signal processing portions configured to determine a calibrated distance to at least one sample.

CROSS REFERENCE TO RELATED APPLICATION(S)

This application is a continuation of U.S. patent application Ser. No.14/926,750, filed Oct. 29, 2015, which claims the filing benefit of U.S.Provisional Application No. 62/069,917, filed Oct. 29, 2014, and U.S.Provisional Application No. 62/181,820, filed Jun. 19, 2015. Theseapplications are incorporated by reference herein in their entirety andfor all purposes.

FIELD OF THE INVENTION

The present invention generally relates to the field of optical distanceand length metrology and specifically to the field of coherent lengthmetrology and laser radar.

BACKGROUND

Various techniques for precisely measuring distance to objects orthicknesses of objects by optical means are known. These techniquesinclude laser triangulation, conoscopic holography, low-coherenceinterferometry, chromatic confocal point sensing, frequency modulatedcontinuous-wave (FMCW) laser radar, swept-frequency optical coherencetomography, and phase modulation range finding. (See, e.g., M.-D. Amann,et al., “Laser ranging: a critical review of usual techniques fordistance measurement,” Opt. Eng. 40(1) 10-19 (January 2001), F.Blateyron, Chromatic Confocal Microscopy, in Optical Measurement ofSurface Topography, (Springer Berlin Heidelberg) pp 71-106 (2011), C.Olsovsky, et al., “Chromatic confocal microscopy for multi-depth imagingof epithelial tissue,” Biomed Opt Express. May 1, 2013; 4(5): 732-740,G. Y. Sirat et al., “Conoscopic holography,” Opt. Lett. 10, (1985), W.C. Stone, et al., “Performance Analysis of Next-Generation LADAR forManufacturing, Construction, and Mobility,” NISTIR 7117, May 2004, andM. A. Choma, “Sensitivity advantage of swept source and Fourier domainoptical coherence tomography,” Opt. Exp. 11 (18), 2183 (2003).) Thesetechniques offer varying levels and combinations of measurement ranges,precisions, and resolutions.

Optical phase-sensitive detection techniques (also sometimes referred toas “coherent detection techniques”), such as low-coherenceinterferometry, optical coherence tomography and laser radar, can offerextremely high resolution, but face unique challenges in measuringdiffusely scattering surfaces due to speckle, the far-field interferencepattern arising from the multiple scattering centers of a diffusereflector. For relative lateral motion (i.e. motion perpendicular to thelaser beam propagation direction, and thus not a Doppler shift) betweenthe laser beam and a rough surface (with roughness less than the systemresolution), researchers at the National Institute of Standards andTechnology (NIST) recently showed that speckle-induced phase variationsplace a “strong limit” on the achievable range uncertainty and precisionusing the FMCW laser radar technique. (See, E. Baumann, et. al, “Specklephase noise in coherent laser ranging: fundamental precisionlimitations,” Opt. Lett., Vol. 39, Issue 16, pp. 4776-4779 (2014).) Thisreference (“Baumann”) is incorporated herein by reference in itsentirety. The researchers showed that speckle noise resulting fromsurface roughness of a laterally moving surface (or laser beam) leads toa non-Gaussian range distribution with measurement errors that candramatically exceed both the Cramer Rao lower bound and the surfaceroughness amplitude. Motion of the beam location on the sample surfacedegrades measurements significantly compared to the case where eachsuccessive point is measured statically, even to the point whereoutliers during lateral motion approach the system range resolution(given by c/2B, where c is the speed of light and B is the informationbandwidth). As a result, the use of FMCW laser radar for high-precisionsurface imaging at a distance, for instance, is limited to either staticpoint-by-point measurements, spatial averaging, or they must enduredegraded precision when the beam location on the sample surface is inmotion. Unfortunately, such lateral motion is needed for a variety ofapplications including non-contact, in-situ industrial metrology andimpression-based forensics evidence. Baumann identifies the specklenoise problem with no solution. Solutions to the surface roughnessspeckle noise problem are therefore needed.

SUMMARY

A method is provided for measuring distance with improved measurementaccuracy or precision, comprising: producing a first laser output;producing a second laser output; modulating an optical frequency of atleast one of the first laser output or the second laser output;producing a combined beam, which is the combination of the first andsecond laser outputs; directing the combined beam through a plurality ofoptical paths, at least one of the optical paths including a sample, andthe plurality of optical paths being configured to direct at least partof the combined beam onto at least one optical detector to produce aninterference signal; distinguishing the interference signalcontributions that are due to the first laser output from theinterference signal contributions that are due to the second laseroutput; and processing first interference signal contributions that aredue to the first laser output with second interference contributionsthat are due to the second laser output to lessen distance ordisplacement measurement errors that result from surface roughness orfrom dispersion properties of the sample or from dispersion propertiesof the optical path that includes the sample.

The first interference signal contributions may be distinguished fromthe second interference signal contributions by substantially opticallyseparating the first and second laser outputs onto a corresponding firstand second detector.

The first interference signal contributions may be distinguished fromthe second interference signal contributions by electrical bandpassfiltering or digital bandpass filtering.

At least one of the first or second optical frequency modulations may bea carrier optical frequency chirp. Alternatively, at least one of thefirst or second optical frequency modulations may be an optical sidebandchirp;

A carrier optical frequency chirp may be additionally modulated toproduce at least one optical sideband on the optical carrier.

The processing step may include calculating a first signal phase and asecond signal phase as functions of time corresponding to a receivedfirst interference signal and a received second interference signal,manipulating the first interference signal phase and the secondinterference signal phase as a function of time to suppress common-modedistance measurement errors that result from surface roughness ordispersion properties of the sample or of the optical path that includesthe sample, thereby producing a corrected signal phase; and determiningthe distance to the sample with reduced distance errors based on thecorrected signal phase.

The manipulating of the first and second interference signal phases mayinvolve determining the sum or difference of the first interferencesignal phase and the second interference signal phase.

The determination of the first signal phase and second signal phases maybe performed using Hilbert transforms.

The method may further comprise performing corrections to at least oneof the first and second signal phases based on the wavelength and chirprate of the first and second laser outputs to produce a corrected firstand second signal phase.

A system is provided for separating up-chirp and down-chirp componentsof a sideband-modulated FMCW system, comprising: a physical deviceproviding a laser output;

a modulator imparting chirped sidebands on a carrier optical frequencyof the laser output, the chirped sidebands being separated in frequency;a beam splitter configured to split the modulated laser output into afirst local oscillator (LO) portion and a second transmitted portion(TX); a frequency shifter configured to shift either or both of the LOand the TX in optical frequency in order to allow separation of thecontributions of the chirped sidebands; a combiner configured to combinethe LO and a receiver portion (RX); a detector configured to detect theinterference signal resulting from the LO and the RX; and a processorconfigured to distinguish the interference signal contributions that aredue to different chirped sidebands and to use the separated interferencesignal contributions to determine a target range.

A method is provided of processing distance measurements to improvemeasurement accuracy or precision, comprising: producing a laser output;modulating the optical frequency of the laser output or modulating asideband of the optical frequency of the laser output to produce amodulated laser output; directing the modulated laser output through aplurality of optical paths at least one of the optical paths including asample, the plurality of optical paths being configured to direct atleast part of the modulated laser output onto at least one opticaldetector to produce an interference signal; computing deviations of theinterference signal amplitude, frequency, or phase from establishedamplitude, frequency, or phase functions or values in either thefrequency domain or the time domain; identifying, weighting, ordisregarding distance measurements based one or more metrics thatquantify the computed deviations from the established amplitude,frequency, or phase functions or values; and utilizing theidentification, weighting, or disregarding of measurements to improvethe accuracy of one or more distance measurements to the sample.

The range peak shape in the frequency domain may be compared to anexemplary range peak shape. The root-mean-square deviations of thesignal phase as a function of time may be compared to an establishedvalue. The signal-to-noise ratio may be compared to an establishedsignal-to-noise ratio value.

A method is provided of processing distance measurements to improvemeasurement accuracy or precision, comprising: producing a first laseroutput; producing a second laser output; modulating at least one of afirst optical frequency of the first laser output, and a second opticalfrequency of the second laser output; producing a combined beam which isthe combination of the first and second laser outputs; directing thecombined beam through a plurality of optical paths, at least one of theoptical paths including a sample, the plurality of optical paths beingconfigured to direct at least part of the combined beam onto at leastone optical detector to produce an interference signal; distinguishingthe interference signal contributions that are due to the first laseroutput from the contributions that are due to the second laser outputwherein the interference signals result from laser outputs for whichdispersion in the sample or the optical path to the sample aresubstantially the same; and processing the first and second interferencesignals to determine the distance to the sample with reduceddispersion-induced distance errors.

At least one of the laser outputs may be modulated with a linear chirp;

The processing may include calculating a first and a second signal phaseas a function of time corresponding to the received first and secondinterference signal; and calculating the sum or difference of the firstand the second signal phases as a function of time to substantiallysuppress common-mode measurement errors and to produce a correctedsignal phase.

The first interference signal and the second interference signal mayresult from the same laser output, but at different times.

The first interference signal may result from a first laser output andthe second interference signal may result from a second laser output.

DESCRIPTION OF THE DRAWINGS

FIG. 1A is a diagram 100 showing some principle elements of a sweptfrequency metrology system according to disclosed embodiments;

FIG. 1B is a plot showing a linearly swept LO and time-delayed Rxoptical frequencies as functions of time according to disclosedembodiments;

FIG. 2A is a plot of range profile data of a brushed alloy sampleshowing the peaks from two measurements (an up chirp and a down chirp)from the same target surface according to disclosed embodiments;

FIG. 2B is a plot of range measurement data of a brushed alloy sampleaccording to disclosed embodiments;

FIG. 3 is a plot of a discretized sample plane with Gaussian measurementbeam according to disclosed embodiments;

FIG. 4A is a plot showing frequency versus time for first and secondlasers according to disclosed embodiments;

FIG. 4B is a plot showing phase versus time for a stationary sample. Inthis case the phase with and without speckle noise are nearly identicalaccording to disclosed embodiments;

FIG. 4C is a plot showing phase versus time of the measured signals fora sample with lateral motion. φ1,0 and φ2,0 represent the phase withoutspeckle-induced phase noise, while φ1 and φ2 represent the measuredphase with speckle-induced noise according to disclosed embodiments;

FIG. 5A is a plot showing an example of simultaneous measurement of upand down chirps without frequency offset showing that f_(beat) is thesame for the up and down chirps according to disclosed embodiments;

FIG. 5B is a plot showing an example of simultaneous measurement of upand down chirps with frequency offset showing that f_(beat) is thedifferent for the up and down chirps according to disclosed embodiments;

FIG. 5C is a simplified block diagram showing components in a chirpedsideband modulation setup. An AOM is used to shift the LO (or Tx) off DCand thereby isolate speckle information from range information accordingto disclosed embodiments;

FIG. 6A is a plot showing filtered (black) and unfiltered (gray) FMCWrange errors for two different surfaces undergoing lateral motion of 50mm/s with respect to the measurement beam. 4901 measurements from a ˜2μm surface roughness piece of ground glass according to disclosedembodiments;

FIG. 6B is a plot showing filtered (black) and unfiltered (gray) FMCWrange errors for two different surfaces undergoing lateral motion of 50mm/s with respect to the measurement beam. 2000 measurements from abusiness card with ˜25 μm surface roughness according to disclosedembodiments;

FIG. 7 is a plot showing an example of threshold settings for the phaseRMSE and peak SNR filter according to disclosed embodiments; and

FIG. 8 is a block diagram showing components used in one embodiment tocompensate for Doppler and speckle phase noise.

DETAILED DESCRIPTION

The invention described herein teaches how multiple opticalphase-sensitive measurements can be made of a surface and used tosignificantly suppress phase noise-induced distance measurement errorsduring lateral motion, such as those due to speckle. In each embodimentdescribed, a difference in phase-sensitivity to the sample surfacedistance between the multiple measurements is used to suppress the phasenoise-induced errors.

A measurement may be defined as the time-varying phase of theinterference between light received from a reference surface and asample surface for a single laser. It is understood that additionalsurfaces and lasers may also be considered. A depiction of a system thatmay perform two simultaneous measurements using two separate lasers isshown in FIG. 1A. Below is a mathematical description of the signal fora single measurement that may follow the formalism provided in Z. W.Barber, et al., “Accuracy of active chirp linearization for broadbandfrequency modulated continuous wave ladar,” Appl. Opt., 49, 213 (2010).The light received from the reference surface will be referred to as thelocal oscillator (LO). The time-varying optical frequency for LOelectric field can be represented in the form

E _(LO)(t,z=0)=E ₀ e ^(−i(ω) ⁰ ^(t+1/2αt) ² ⁾,  (1)

where ω₀ is the angular optical frequency at the beginning of the chirp,and α is the angular chirp rate. Propagation of the LO field to thesample surface can be treated by performing a Fourier transform to thefrequency domain.

$\begin{matrix}{{E\left( {\omega,{z = 0}} \right)} = {{\frac{E_{0}}{\sqrt{2\pi}}{\int_{- \infty}^{\infty}{e^{- {i{({{\omega_{0}t} + {\frac{1}{2}\alpha \; t^{2}}})}}}e^{i\; \omega \; t}{dt}}}} = {E_{0}\frac{1 - i}{\sqrt{2\alpha}}e^{\frac{{i{({\omega - \omega_{0}})}}^{2}}{2\alpha}}}}} & (2)\end{matrix}$

The LO field is then propagated to the sample surface and back to thereference surface, where it interferes with the LO field, by applying aTaylor expanded form of the propagator e^(iβz).

E _(Rx)(ω,z=2R)=E(ω,z=0)e ^(i2β) ⁰ ^(R) e ^(i2β) ¹ ^((ω-ω) ⁰ ^()R) e^(i2β) ² ^((ω-ω) ₀ ⁾ ² ^(R)  (3)

Here R is the distance to the sample and

${\beta_{0} = \frac{\omega_{0}n}{c}},{\beta_{1} = {\left. \frac{\partial\beta}{\partial\omega} \right|_{\omega = \omega_{0}} = \frac{1}{v_{g}}}},{{{and}\mspace{14mu} \beta_{2}} = \left. \frac{\partial^{2}\beta}{\partial\omega^{2}} \middle| {}_{\omega = \omega_{0}}. \right.}$

Also, c is the speed of light, n is the refractive index of the mediumbetween the reference and sample surfaces, and v_(g) is the groupvelocity in the medium. The time-domain description of the fieldreflected from sample surface, back to the LO surface, is given by

$\begin{matrix}{{{E_{Rx}\left( {t,{z = {2\; R}}} \right)} = {E_{0}\sqrt{\frac{\alpha^{\prime}}{\alpha}}e^{- {i{({{\omega_{0}{({t - {2\frac{n}{c}R}})}} + {\frac{1}{2}{\alpha^{\prime}{({t - {2\beta_{1}R}})}}^{2}}})}}}}},} & (4)\end{matrix}$

where

$\alpha^{\prime} = {\frac{\alpha}{1 + {2\; R\; {\alpha\beta}_{2}}}.}$

The interference between the fields E_(LO) and E_(Rx) comprises a singledistance measurement, and takes the form

$\begin{matrix}{{S(t)} \sim {{E_{LO}\left( {t,{z = 0}} \right)}{E_{Rx}\left( {t,{z = {2\; R}}} \right)}} \sim {e^{- {i{({{2\omega_{0}\frac{n}{c}R} - {\frac{1}{2}{\alpha^{\prime}{({2\beta_{1}R})}}^{2}} + {2\; R\; \alpha^{\prime}\beta_{1}t} + {\frac{1}{2}{({\alpha - \alpha^{\prime}})}t^{2}}})}}}.}} & (5)\end{matrix}$

For many cases, terms involving β₂ and β₁ ² can be neglected, and thesignal can be adequately approximated by

$\begin{matrix}{{S(t)} \sim {e^{- {i{({{2{\omega 0}\frac{n}{c}R} + {2\; R\; {\alpha\beta}_{1}t}})}}}.}} & (6)\end{matrix}$

However, we have included terms to second order in equation (5) to aidthe discussion in later sections of this document.

FMCW Carrier Measurements for Compensating Phase Noise-Induced Errors

FIG. 1A is a diagram showing some principle elements of a sweptfrequency metrology system 100 according to disclosed embodiments. InFIG. 1A, black arrows indicate optical paths.

As shown in FIG. 1A, the swept frequency metrology system 100 includes afirst frequency-chirped laser 110, a second frequency-chirped laser 115,a beam combiner 120, a circulator 130, a reference surface 135, a firstsample surface 140, and a detection and processing unit 150.

The first frequency-chirped laser 110 and the second frequency-chirpedlaser 115 each output light of an optical frequency that changessubstantially linearly (chirps) in time over a given chirp duration.

The beam combiner 120 is configured to receive and combine at least partof the first and second laser outputs into a combined laser output. Insome embodiments, a single laser may produce an output with bothfrequency-chirped components, in which case the beam combination occursinternal to the laser.

The combined laser output from the beam combiner 120 is then directedthrough the circulator 130 and a plurality of optical paths configuredto direct at least part of the combined beam onto an optical detector toproduce an interference signal.

In FIG. 1A, an optical path may include a transmitted portion denotedTx. An optical path may include reflection from the reference surface135, the reflected portion from the reference surface 135 being denotedLO. An optical path may include reflection from the first sample surface140, the reflected portion from the first sample surface 140 beingdenoted Rx.

A sum of LO and Rx is directed to the detection and processing circuitto determine the distance measurement, as noted below.

FIG. 1B is a plot 150 showing a linearly swept LO and time-delayed Rxoptical frequencies as functions of time according to disclosedembodiments.

In some embodiments of the invention, the optical phase-sensitivemeasurements may be performed using the FMCW ladar technique, and wherethe optical carrier may be linearly swept, or “chirped”, in time.“Performance Analysis of Next-Generation LADAR for Manufacturing,Construction, and Mobility,” (cited above) describes the FMCW chirpedladar technique and is incorporated herein by reference in its entirety.A simplified block diagram showing a setup that may be used tocompensate speckle noise is shown in FIG. 1A, the laser radiation fromtwo frequency-chirped lasers (one for each optical phase-sensitivemeasurement) may be combined, directed through an optical circulator,and transmitted (Tx) toward a sample surface. A portion of the combinedlight (LO) may be reflected from a reference surface, while a secondportion (Rx) may be reflected from a sample surface. Interference mayoccur between light reflected from the reference and sample surfaces.The distance between the reference and sample surfaces may be determinedby measuring the frequency of the heterodyne beat generated by theinterferometric combination of the Rx and LO resulting from either ofthe two frequency-swept lasers. As shown in FIG. 1B for a single laser,the beat frequency is given by the equation f_(beat)=κτ, whereκ=α/2π=B/τ_(chirp) is the chirp rate (B is the chirp bandwidth andτ_(chirp) is the chirp temporal duration), and τ=2Rn_(g)/c is the timedelay between the Rx and LO chirp waveforms where n_(g) is the groupindex of the measurement path. Solving for R as a function of f_(beat)allows for determination of the range by measuring the heterodyne beatfrequency.

However, when the sample surface is rough, using the measurement of thedistance from just one of the frequency-swept lasers may result indistance errors due to speckle. These errors may increase dramaticallywhen the sample surface is translated perpendicularly to the beampropagation direction (e.g. scanning the beam across the surface or viceversa). FIG. 2A shows an FMCW range profile resulting from one surfaceand from two lasers with different chirp rates. FIG. 2B shows thedetermination of range from such a range profile for 100 consecutiverange measurements of a brushed alloy surface (with sub-resolved surfaceroughness) using an FMCW chirped ladar system with resolution(full-width at half max) of approximately 1.5 mm. The plus and circlesymbols in FIG. 2B represent the distance measurements when only oneoptical phase-sensitive measurement (data from one laser) is used. InFIG. 2B, the sample remained stationary for the first 28 measurements,and then was laterally translated for the remaining measurements. Thenearly two order of magnitude increase in distance measurement errorsobserved during lateral motion confirm the observations made by the NISTresearchers.

FIG. 2A is a plot 200 of range profile data of a brushed alloy sampleshowing the peaks from two measurements (an up chirp and a down chirp)from the same target surface.

FIG. 2B is a plot 250 of range measurement data of a brushed alloysample. Sample lateral motion begins after the 28th data point. Circlesand pluses represent range measurements using either down or up chirps.Square data points represent range measurements that combine data fromthe up and down chirps resulting in speckle-compensated measurements.

Measurement Method

To solve the problem noted above, the disclosed embodiments teach howthe use of two simultaneous distance measurements with different phasesensitivities on the surface distance can mitigate the speckle and otherphase noise effects. In some embodiments of the invention, the differentphase sensitivities are achieved by chirping the two lasers at differentchirp rates. Even though both lasers are used to measure a singledistance, for one chirp rate, the phase of the received signal evolvesat one rate in time, while for the second chirp, the phase of thereceived signal evolves at a different rate in time. Conversely, it isimportant to note that the phase noise caused by speckle is common-modefor the two measurements, and can therefore be removed while maintainingthe distance information. The measurement setup shown in FIG. 1A allowsa single detector and single digitizer to acquire the sample surfacedistance information from both lasers simultaneously because K, andtherefore f_(beat), is different for the two lasers. The different rangepeak frequencies for the two measurements, shown in FIG. 2A, highlighthow the two measurements exhibit different optical phase-sensitivity tothe sample surface distance. The ‘+’ points in FIG. 2B represent therange measurement results from the first chirp rate, the ‘o’ pointsrepresent the same for the second chirp rate, and the black squarepoints are the speckle-compensated results from combining the phaseinformation from the first and second chirps, as described below. It isclear from closer inspection of the data that the ‘+’ and ‘o’ data areanti-correlated. The algorithm described below capitalizes on thisanti-correlation to compensate the speckle-induced phase noise.

The following is a mathematical description for speckle phase errorcompensation of FMCW laser radar measurements from a diffuse target withsurface roughness σ_(z), where σ_(z)<<ΔR, and ΔR=c/2B is the distancemeasurement resolution. The mathematical model relies on discretizingthe sample plane into a uniform grid of j cells, and assigning a randomheight z_(j) to each grid cell as shown in FIG. 3. For simplicity, wewill let n=n_(g)=1 in following description.

FIG. 3 is a plot 300 of discretized sample plane with Gaussianmeasurement beam according to disclosed embodiments.

The measured FMCW distance signal is a sum of the returns from each gridcell in the sample plane,

$\begin{matrix}{{{S(t)} = {\sum_{j}{e^{\lbrack{{{- {({{({x_{j} - x_{0}})}^{2} + {({y_{j} + y_{0}})}^{2}})}}/2}\; w_{0}^{2}}\rbrack}e^{\lbrack{\frac{4\pi \; i}{c}{z_{j}{({v_{0} + {\kappa \; t}})}}}\rbrack}}}},} & (7)\end{matrix}$

where κ is the laser chirp rate, v₀ is the laser start frequency, andz_(j) is the distance to the j^(th) grid cell. One can express equation(7) in polar form as,

$\begin{matrix}{{{S(t)} = {{A(t)}e^{\lbrack{{\frac{4\pi \; i}{c}{z_{0}{({v_{0} + {\kappa \; t}})}}} + {\Theta {(t)}}}\rbrack}}},} & (8)\end{matrix}$

where

${z_{0} = {\frac{1}{N}{\sum_{j}z_{j}}}},$

and Θ(t) and A(t) are defined by equation (7). (See, P. Pavlicek, et.al. “Theoretical measurement uncertainty of white-light interferometryon rough surfaces,” Appl. Opt. 42, 1809-1813 (2003).) Due to the smallsurface roughness, and in the limit that the measurement bandwidth issmall compared to the laser frequency v₀, the phase and amplitudefunctions can be approximated by first order Taylor expansions:Θ(t)≈Θ₀+Θ₁t, and A(t)≈A₀+A₁t. In this regime, the range errors due tospeckle take the form, δz=c/2πκΘ₁−z₀. Equations (7) and (8) weredeveloped to describe the complicated behavior of the amplitude andphase of coherent distance measurements from diffuse surfaces.References Baumann and Pavlicek both describe the degradation of theirrespective measurements due to speckle from diffuse surfaces, but offerno solutions for compensating the measured phase errors. In thefollowing paragraphs we will describe how to use two FMCW laser radarmeasurements with different sensitivities of the phase to the sampledistance to compensate speckle-induced phase errors.

FIG. 4A is a plot 400 showing frequency versus time for first and secondlasers according to disclosed embodiments.

FIG. 4B is a plot 430 showing phase versus time for a stationary sample.In this case the phase with and without speckle noise are nearlyidentical according to disclosed embodiments.

FIG. 4C is a plot 470 showing phase versus time of the measured signalsfor a sample with lateral motion. φ_(1,0) and φ_(2,0) represent thephase without speckle-induced phase noise, while φ₁ and φ₂ represent themeasured phase with speckle-induced noise according to disclosedembodiments.

FIGS. 4A-C illustrate conceptually the behavior of speckle-induced phaseerrors for a two-laser FMCW distance measurement in scenarios withstationary and laterally moving samples. FIG. 4A shows the frequencychirp for both lasers. FIG. 4B shows the phase versus time for each FMCWrange measurement for a stationary sample. In this case the timeevolution of the speckle phase Θ(t) is entirely due to thetime-rate-of-change of the laser frequency. For typical values of thechirp bandwidth (B>100 GHz) and surface roughness (<30 μm) the measuredspeckle-induced range noise due to the time-rate-of change of the laserfrequency is small, on the order of the surface roughness. FIG. 4C showsthe phase versus time for each FMCW range measurement when the sample ismoving laterally. If the sample surface were specular (i.e. withoutspeckle noise) the measured phase would evolve linearly with a slopethat is proportional to the sample range as represented by φ_(1,0) andφ_(2,0), and there would be no error in the distance measurement. Whenthe sample surface is diffuse the speckle phase (Θ_(0.1) and Θ_(0.2))evolves rapidly due to the changing position of the surface featuresrelative to the measurement beam leading to large changes in theinterference between returns from the individual grid cells shown in theleft side of FIG. 3.

Without compensation, these phase excursions can result in range errorsthat are on the order of the distance measurement resolution ΔR=c/2B.

This case can be described by equation (8), with first order Taylorexpansions of the phase and amplitude functions, for time intervalswhere the phase fluctuations Θ are approximately linear. The entiremeasurement duration is then modeled by combining many sequentialregions defined by first-order Taylor expansions in Θ and A. If the twolasers are sufficiently close in wavelength, and the surface roughnessis sufficiently small, the speckle phases for the two measurements areapproximately equal at every point in time [Θ₁(t)≈Θ₂(t)]. The conditionfor measuring correlated speckle phase with lasers 1 and 2 is providedin equation (9).

$\begin{matrix}{{\frac{2\pi {{\lambda_{2} - \lambda_{1}}}}{\left( \frac{\lambda_{2} + \lambda_{1}}{2} \right)^{2}}\sigma_{z}}1.} & (9)\end{matrix}$

Finally, the phases from the two separate measurements may be combinedto form a “compensated phase” whose range may depend only on the averagedistance to the sample z₀, and the two laser chirp rates. A linear fitof the compensated phase may then be performed to extract the phaseslope (e.g. the angular frequency) of the compensated range peak fromwhich the distance measurement may be calculated. These steps are shownmathematically in equations (10) and (11).

$\begin{matrix}{\varphi_{comp} = {{{\varphi_{2}(t)} - {\varphi_{1}(t)}} = {{\frac{4\pi \; z_{0}}{c}\left( {v_{2} + {\kappa_{2}t}} \right)} + {\Theta_{2}(t)} - {\frac{4\pi \; z_{0}}{c}\left( {v_{1} + {\kappa_{1}t}} \right)} - {{\Theta_{1}(t)}.}}}} & (10) \\{\mspace{79mu} {z_{m} = {\frac{\left( {{phase}\mspace{14mu} {slope}} \right)c}{4\pi}{\left( \frac{1}{\kappa_{2} - \kappa_{1}} \right).}}}} & (11)\end{matrix}$

Chirped Sideband FMCW

FIG. 5A is a plot 500 showing an example of simultaneous measurement ofup and down chirps without frequency offset showing that f_(beat) is thesame for the up and down chirps according to disclosed embodiments.

FIG. 5B is a plot 530 showing an example of simultaneous measurement ofup and down chirps with frequency offset showing that f_(beat) is thedifferent for the up and down chirps according to disclosed embodiments.

FIG. 5C is a simplified block diagram showing components in a chirpedsideband modulation setup 570. An AOM is used to shift the LO (or Tx)off DC and thereby isolate speckle information from range informationaccording to disclosed embodiments.

As shown in FIG. 5C, the chirped sideband modulation set up 570 includesa laser 572, a waveform generator 574, an electro-optic modulator 576, asplitter 578, a circulator 580, an acousto-optic modulator 582, anacousto-optical modulator signal generator 584, a target 586, a combiner588, and a detection and processing unit 590.

In some embodiments of the invention, the optical phase-sensitivemeasurements may be performed using the FMCW ladar technique, and wherethe waveforms used may include frequency-chirped sideband modulation(i.e. homodyne rather than heterodyne) following U.S. Pat. No. 7,742,152“Coherent Detection Scheme for FM Chirped Laser Radar”. U.S. Pat. No.7,742,152 is incorporated herein by reference in its entirety. In U.S.Pat. No. 7,742,152, the authors describe a “signal fading” problem thathinders the measurements during motion. We have determined that thissignal fading is a result of the fact that, while two phase-sensitivemeasurements are present, the two measurements cannot be easilydistinguished. This is because the two phase-sensitive measurementsutilize sideband chirps with opposite signs (i.e. one is increasing infrequency and one is decreasing in frequency), but the same chirp ratemagnitude. In this case, the “up” and “down” frequency chirps aremeasured at common or similar RF frequencies because the measurementsare performed symmetrically about DC. As shown in FIG. 5A, f_(beat) isthe same for both the up and down frequencies. When using the samedetector, the signals received from the up and down chirps can thereforeinterfere, resulting in “signal fading”. As a result, the demonstratedmeasurements can suffer from phase-noise errors during surface (or beam)movement.

To separate and utilize the two phase-sensitive measurements, thedisclosed embodiment shows that by shifting the measurement off of DC,the up and down chirps can be made to not share similar RF frequenciesand the measurements can be made without signal fading because theydon't interfere with one another.

FIG. 5A discloses an embodiment to accomplish the shifting of themeasurement off of DC. Light from a laser 572 is directed through anelectro-optic modulator 576 that produces chirped sidebands on theoptical carrier frequency of the laser. The electro-optic modulator 576is driven by a waveform generator 574. The modulated light is receivedby a splitter 578, which outputs a local oscillator (LO) and atransmitted (Tx) portion. The Tx portion is directed through an opticalcirculator 580 to a target 586. Light returning (Rx) from the target isredirected and received by a beam combiner 588. The LO portion isdirected through an acousto-optic modulator 582 to allow separation ofthe contributions from the up-chirped and down-chirped sidebands. Theacousto-optic modulator is driven by an acousto-optic modulator signalgenerator. The frequency-shifted LO is also received by the beamcombiner. Output from the beam combiner is directed to a detection andprocessing unit 590.

In FIG. 5B, we show the result of shifting the Tx beam with an opticalmodulator. In this case, f_(beat) is shown to be different for the upand down chirps. A simplified example chirped sideband modulationembodiment is shown in FIG. 5C that has been used to solve the signalfading problem and suppress phase noise-induced distance measurementerrors. The figure shows the use of an acousto-optic modulator (AOM) inthe LO path to enable the separation of the up and down chirpinformation. In the example shown one may use the RF frequencies belowf_(offset) to detect the down chirp signals and above f_(offset) todetect the up chirp signals. Once the up and down chirps are separated,the suppression of phase noise-induced distance measurement errorsfollows analogously as for the carrier chirp case described in theprevious section. Again, the different chirp rates (one positive and onenegative in this case) provide the different optical phase sensitivitiesfor suppression of the phase noise-induced distance measurement errors.

Measurement Filtering

The non-specular reflectivity of diffuse surfaces introduces thepossibility for multipath interference in FMCW measurements of roughsurfaces. Multipath interference refers to secondary reflections orscattering of the measurement beam between two or more surface featuresthat may ultimately scatter back into the receiver. Multipathinterference may cause time-varying phase shifts that result in errorsin FMCW range measurements. These errors may become more pronounced whenthe sample undergoes lateral motion due to the rapid phase evolution ofthe interfering reflections. Specifically, large range errors may beobserved in cases where the separation between the contributing surfacefeatures is sufficiently large that the inequality expressed in equation(9) is no longer valid. In such cases, the speckle-induced phase may notbe well compensated by the measurement approach described in theprevious section, and the resulting FMCW range measurement can exhibiterrors on the order of the FMCW range resolution. FMCW measurements madeon several types of rough surfaces indicate that the locations wheremultipath interferences occur, the spatial frequency of these effects,and the magnitude of the measurement errors may have the followingproperties: Their locations and magnitudes may be repeatable; thespatial frequency and magnitude of the errors are dependent on thematerial type; and the statistics of resulting range errors may not beGaussian. Measurements of Lambertian scattering materials may exhibitmore frequent and larger magnitude range errors while measurements ofpseudo-diffuse materials, those that appear diffuse at low observanceangles but reflective at high observance angles, yield less frequent andsmaller magnitude range errors. Examples of range errors due tomultipath interference are shown in FIG. 6A for ground glass and FIG. 6Bfor a paper business card.

FIG. 6A is a plot 600 showing filtered (black) and unfiltered (gray)FMCW range errors for two different surfaces undergoing lateral motionof 50 mm/s with respect to the measurement beam according to disclosedembodiments. 4901 measurements from a ˜2 μm surface roughness piece ofground glass. The filter threshold is set to reject ˜25% of themeasurements. The filtered data set (black) contains 9 points with rangeerrors exceeding 25 μm while the unfiltered set (gray) contains 121points with range errors exceeding 25 μm.

FIG. 6B is a plot 650 showing filtered (black) and unfiltered (gray)FMCW range errors for two different surfaces undergoing lateral motionof 50 mm/s with respect to the measurement beam according to disclosedembodiments. 2000 measurements from a business card with ˜25 μm surfaceroughness. The filtered data set (black) contains 2 points with rangeerrors exceeding 250 μm while the unfiltered set (gray) contains 71points with range errors exceeding 250 μm. The difference in thefrequency and magnitude of the range errors between the two materials isdue to the fact that ground glass is pseudo-diffuse while the businesscard is a Lambertian scatterer.

Fortunately, measurements that exhibit large range errors due tomultipath interference contain signatures that may allow for detectionof the errors. Once detected the errors may either be weighted orremoved from the data set.

The disclosed embodiments teach two filtering methods to detectmeasurements containing large range errors. Both methods rely on theidea that peaks containing interference from multiple unresolved surfacefeatures may often be deformed as a result of the multi-surfaceinterference, compared to an ideal single specular reflection. Oneembodiment uses peak shape analysis to detect misshapen peaks. In thisembodiment, the FMCW range peak may first be fit with a Gaussian orother appropriate function. Next, the root-mean-squared error (RMSE)between the measured peak and the fit function may be computed. Finally,the RMSE is compared against a threshold value to identify peakscontaining large range errors. In situations where multiple rangemeasurements are averaged, the threshold value may be computed based onthe statistics of the RMSE values for the set of points being averaged.In single-point measurement scenarios the threshold may be computed inthe same way as for averaged measurements using the assumption that theaverage peak SNR changes slowly compared to the measurement rate.

FIG. 7 is a plot 700 showing an example of threshold settings for thephase RMSE and peak SNR filter according to disclosed embodiments.

The second embodiment for filtering compares the range peak SNR and theRMSE of the signal phase to detect misshapen range peaks. Thisembodiment was used to filter both data sets shown in FIG. 6, and itsimplementation is illustrated in FIG. 7. For this embodiment, the SNR ofthe range peak may first be computed. Next, the instantaneous phase ofthe signal may be computed as a function of time. If the measured signalis real-valued, this step may be carried out using a Hilbert Transformto derive the complex-valued representation. The instantaneous phase maythen be computed from the complex-valued signal using the tangentfunction. The phase is unwrapped yielding a phase versus time curve thatis approximately linear. The phase curve may then be fit with alow-order polynomial, and the RMSE between the fit line and the measuredvalues may be computed. Finally, peaks containing large range errors maybe identified by comparing the measured peak SNR and phase RMSE againstthreshold values, as shown in FIG. 7.

The data sets in FIG. 6 demonstrate the benefits of this type offiltering. In each case the number of outlier measurements is reduced bymore than a factor of 10, and the standard deviation of each data set isreduced by nearly a factor of 2. During initial testing both filteringmethods achieved similar performance, and the preferred approach (orcombination of approaches) may depend on the specific measurementscenario and the details of the signal processing work flow.

Dispersion Compensation of FMCW Measurements

In measurement scenarios where the target, the beam delivery optics, orthe optical medium between the reference surface and sample surface hasdispersion the ½(α−α′)t² term in equation (5) may become significant,and the dispersion may require compensation to produce accurate distancemeasurements. Fortunately, compensation of such measurements can beachieved by averaging an up-chirp and down-chirp measurement that coverroughly the same spectral region, and have approximately the same, butopposite sign, chirp rate. In practice this can be accomplished byaveraging temporally sequential up and down chirps from the same chirpedlaser source. This technique will be illustrated by considering ameasurement where the reference surface and the sample surface areseparated by 0.5 m of SMF-28 fiber. The dispersion coefficient forSMF-28 is β₂=−0.022 ps²/m, and the group velocity is v_(g)=c/1.4682 at1550 nm. For this example the measurement duration will be 200 ps, andthe chirp rate will be 600 MHz/ps. At the end of the measurement(t_(c)=200 is) the up-chirp (e.g. α_(up)>0) will have accumulated anFMCW phase of φ_(u)=α_(u)β₁zt_(c)+½(α_(u)−α_(u)′)t_(c) ². Theaccumulated phase for each term in φ_(u) is given byα_(u)β₁zt_(c)=3669.4 rad, and ½(α_(u)−α_(u)′)t_(c) ²=0.0063 rad. That½(α_(u)−α_(u)′)t_(c) ²>0 reflects the fact that α_(u)>α_(u)′ for theup-chirp. For the down-chirp the accumulated FMCW phase at the end ofthe measurement follows the same relation,φ_(d)=α_(d)β₁zt_(c)+½(α_(d)−α_(d)′)t_(c) ². However, for the down-chirpα_(d)β₁zt_(c)=−3669.4 rad, whereas ½(α_(d)-α_(d)′)t_(c) ²=0.0063 rad. Wecan now use equation (11) to calculate the distance between thereference and sample surfaces. Due to the dispersion phase term theup-chirp measurement appears too long by ˜2 ppm, and the down-chirpmeasurement appears too short by ˜2 ppm. However, the averaged distancemeasurement,

${z = {\frac{\left( {\phi_{u} - \phi_{d}} \right)v_{g}}{2\; {t_{c}\left( {\alpha_{u} - \alpha_{d}} \right)}} = {0.5\mspace{14mu} m}}},$

provides the correct answer.

Using Phase Reconstruction to Compensate Phase Noise-Induced DistanceMeasurement Errors

As described in previous sections, compensation of phase-noise-induceddistance measurement errors due to speckle for coherent ladarmeasurements may be important for obtaining accurate and precisemeasurements of dynamic and diffuse targets. In this section, wedemonstrate an effective method for accomplishing the processinginvolved with this compensation using phase reconstruction, as shown inFIG. 8. For one embodiment of this invention, we may simultaneouslyacquire heterodyne beat signals resulting from a sample surface usingtwo different chirp rates. As an exemplary case, an up-chirp and adown-chirp, as represented by the functions f_(up)(t) and f_(dn)(t), areassumed for the following discussion. We may transform these heterodynebeat signals to recover/reconstruct the signal phases as functions oftime during the measurement, as represented by φ_(up)(t) and φ_(dn)(t).This may be accomplished using methods such as a Hilbert Transform. Ifthe center wavelength or chirp rate is different for the up and downchirps, then one may apply scaling and offset corrections to account forthe differences, as represented by φ_(up)′(t) and φ_(dn)′(t). One maythen average the corrected up-chirp and down-chirp phases as functionsof time to suppress the phase noise, as represented by φ_(avg)(t). Ifdesired, the noise-suppressed time domain oscillating heterodyne beatfunction may be reconstructed from knowledge of the noise-suppressedphase as a function of time, as represented by f_(cor)(t).

FIG. 8 is a block diagram showing components used in a processing chain800 to compensate for Doppler and speckle phase noise according todisclosed embodiments.

As shown in FIG. 8, the processing chain 800 includes an up-chirptime-domain beat determination element 810, an up-chirp phasereconstruction element 820, an element for correction of the up-chirpfor λ and κ differences 830, a down-chirp time-domain beat determinationelement 840, a down-chirp phase reconstruction element 850, an elementfor correction of the down-chirp for λ and κ differences 860, anaveraging element 870 for averaging up and down phases, and aconstruction element 880 for constructing a corrected signal. Thesevarious elements 810-880 could be implemented as electrical circuits ordigital processing.

The up-chirp time-domain beat determination element 810 is configured todetermine an up-chirp time-domain beat f_(up)(t).

The up-chirp phase reconstruction element 820 is configured toreconstruct an up-chirp phase φ_(up)(t) based on the up-chirptime-domain beat f_(up)(t).

The element for correction of the up-chirp for λ and κ differences 830is configured to correct the up-chirp phase reconstruction φ_(up)(t)based on λ and κ differences to generate a corrected up-chirp phasereconstruction φ′_(up)(t).

The down-chirp time-domain beat determination element 840 is configuredto determine a down-chirp time-domain beat f_(down)(t)

The down-chirp phase reconstruction element 850 is configured toreconstruct a down-chirp phase φ_(down)(t) based on the down-chirptime-domain beat f_(down)(t).

The element for correction of the down-chirp for λ and κ differences 860is configured to correct the down-chirp phase reconstruction φ_(down)(t)based on λ and κ differences to generate a corrected down-chirp phasereconstruction φ′_(down)(t).

The averaging element 870 is configured to average the correctedup-chirp phase reconstruction φ′_(up)(t) and the corrected down-chirpphase reconstruction φ′_(down)(t) to generate an average phasereconstruction φ_(avg)(t).

The construction element 880 is configured to construct a correctedsignal f_(corr)(t) based on the average phase reconstruction φ_(avg)(t).

What is claimed is:
 1. A method for determining a distance to at least aportion of a diffusely scattering object, comprising: generating a firstlaser output; generating a second laser output, wherein at least one ofthe first laser output or the second laser output comprises a modulationsideband; chirping an optical frequency of at least one of the firstlaser output or the second laser output to generate a first output beamand a second output beam; generating a first local oscillator beam thatexhibits a chirp waveform of the first output beam; generating a secondlocal oscillator beam that exhibits a chirp waveform of the secondoutput beam; directing at least a portion of the first output beam and aportion of the second output beam to at least a portion of a diffuselyscattering object at least in part during motion of the diffuselyscattering object relative to the portion of the first output beam, theportion of the second output beam, or both output beams; receiving ascattered portion of the first output beam from the diffusely scatteringobject to form a first received beam; receiving a scattered portion ofthe second output beam from the diffusely scattering object to form asecond received beam; directing at least a portion of the first receivedbeam and at least a portion of the first local oscillator beam onto anoptical detector to produce a first interference signal; directing atleast a portion of the second received beam and at least a portion ofthe second local oscillator beam onto the optical detector or adifferent optical detector to produce a second interference signal; andprocessing the first interference signal and the second interferencesignal to determine a distance to at least a portion of the diffuselyscattering object.
 2. The method of claim 1, further comprising:generating the first laser output and the second laser output at a samelaser source.
 3. The method of claim 1, further comprising: using anoptical modulator to generate the one or more modulation sidebands. 4.The method of claim 1, wherein said motion comprises lateral motion,axial motion, or a combination thereof.
 5. The method of claim 1,wherein said directing at least a portion of the first output beam and aportion of the second output beam to at least a portion of a diffuselyscattering object is performed using a beam scanning device or a beamsteering device.
 6. A method for determining a distance to at least aportion of an object, comprising: generating a first laser output;generating a second laser output, wherein the first and second laseroutputs may be derived from the same laser source or from differentlaser sources; chirping an optical frequency of at least one of thefirst laser output or the second laser output to generate a first outputbeam and a second output beam; generating a first local oscillator beamthat exhibits a chirp waveform of the first output beam; generating asecond local oscillator beam that exhibits a chirp waveform of thesecond output beam; directing at least a portion of the first outputbeam and a portion of the second output beam to at least a portion of anobject; receiving a scattered or reflected portion of the first outputbeam from the object to form a first received beam; receiving ascattered or reflected portion of the second output beam from the objectto form a second received beam; directing at least a portion of thefirst received beam and at least a portion of the first local oscillatorbeam onto an optical detector to produce a first interference signal;directing at least a portion of the second received beam and at least aportion of the second local oscillator beam onto the optical detector ora different optical detector to produce a second interference signal;and using a first signal phase of the first interference signal and asecond signal phase of the second interference signal to determine adistance to at least a portion of the object.
 7. The method of claim 6,further comprising: calculating said first signal phase or said secondsignal phase based on implementation of a Hilbert transform or othertransform to produce a complex-valued representation of the firstinterference signal or the second interference signal.
 8. The method ofclaim 6, further comprising: calculating said first signal phase or saidsecond signal phase based on a phase of a complex-valued representationof the first interference signal or the second interference signal. 9.The method of claim 6, wherein said using the first signal phase and thesecond signal phase to determine a distance to at least the portion ofthe object comprises determining a sum or a difference of the firstsignal phase and the second signal phase.
 10. The method of claim 6,wherein said using the first signal phase and the second signal phase todetermine a distance to at least the portion of the object comprisesperforming corrections to at least one of the first signal phase or thesecond signal phase, or a combination of the first and second signalphases, based on an optical wavelength, an optical frequency, or a chirprate of at least one of the first output beam or the second output beam.11. The method of claim 6, wherein said using the first signal phase andthe second signal phase to determine a distance to at least the portionof the object comprises performing a linear fit to a signal phaseincluding at least the first signal phase and the second signal phase.12. The method of claim 6, further comprising: modulating, at an opticalmodulator, at least one of the first or second laser outputs to generatea modulation sideband.
 13. A method comprising: generating a first laseroutput; generating a second laser output, wherein the first and secondlaser outputs may be derived from the same laser source or fromdifferent laser sources; chirping an optical frequency of at least oneof the first laser output or the second laser output to generate a firstoutput beam and a second output beam; generating a first localoscillator beam that exhibits a chirp waveform of the first output beam;generating a second local oscillator beam that exhibits a chirp waveformof the second output beam; directing at least a portion of the firstoutput beam and a portion of the second output beam to at least aportion of a diffusely scattering object; receiving a scattered orreflected portion of the first output beam from the diffusely scatteringobject to form a first received beam; receiving a scattered or reflectedportion of the second output beam from the diffusely scattering objectto form a second received beam; directing at least a portion of thefirst received beam and at least a portion of the first local oscillatorbeam onto an optical detector to produce a first interference signal;directing at least a portion of the second received beam and at least aportion of the second local oscillator beam onto the optical detector ora different optical detector to produce a second interference signal;and weighting or filtering a range peak, a signal phase, or aninterference signal based on one or more metrics comprising a shape of arange peak, a shape of a signal phase, or a shape of an interferencesignal.
 14. The method of claim 13, further comprising calculating aFourier transform of the first interference signal or the secondinterference signal to generate one or more range peaks; or calculatinga Hilbert transform or other transform to generate a complex-valuedrepresentation of the first interference signal or the secondinterference signal for generation of one or more signal phases.
 15. Themethod of claim 13, wherein the one or more metrics is based at least ona reference shape of a range peak, a reference shape of a signal phase,a reference shape of an interference signal, a signal-to noise ratio ofa range peak, a signal-to noise ratio of a signal phase, or a signal-tonoise ratio of an interference signal.
 16. The method of claim 13,wherein the directing of at least the portion of the first output beamand the portion of the second output beam comprises directing at leastthe portion of the first output beam and directing the portion of thesecond output beam to at least the portion of the diffusely scatteringobject at least in part during motion of the diffusely scattering objectrelative to the portion of the first output beam, the portion of thesecond output beam, or both output beams.
 17. The method of claim 13,wherein said one or more metrics comprise a root-mean-square deviationof a shape of a range peak, a shape of a signal phase, or a shape of aninterference signal as compared to a reference or calculated shape of arange peak, a reference or calculated shape of a signal phase, or areference or calculated shape of an interference signal, respectively.18. The method of claim 13, further comprising: utilizing at least oneof the one or more metrics to correct a value of a distance measurement.19. The method of claim 13, further comprising: utilizing at least oneof the one or more metrics to quantify a confidence in a distancemeasurement.
 20. A method of determining the distance to at least aportion of an object in the presence of dispersion comprising:generating a first laser output; generating a second laser output;chirping the optical frequency of the first laser output at a firstchirp rate and with a first center wavelength to generate a first outputbeam; chirping the optical frequency of the second laser output at asecond chirp rate and with a second center wavelength to generate asecond output beam, wherein the second center wavelength is selectedsuch that a dispersion imparted on the second output beam is the same asa dispersion imparted on the first output beam; generating a first localoscillator beam that exhibits a chirp waveform of the first output beam;generating a second local oscillator beam that exhibits a chirp waveformof the second output beam; directing at least a portion of the firstoutput beam and a portion of the second output beam to at least aportion of an object, receiving a scattered or reflected portion of thefirst output beam from the object to form a first received beam;receiving a scattered or reflected portion of the second output beamfrom the object to form a second received beam; directing at least aportion of the first received beam and at least a portion of the firstlocal oscillator beam onto an optical detector to produce a firstinterference signal; directing at least a portion of the second receivedbeam and at least a portion of the second local oscillator beam onto theoptical detector or a different optical detector to produce a secondinterference signal; and processing the first interference signal andthe second interference signal to determine a distance to at least aportion of the object.
 21. The method of claim 20, wherein saidprocessing the first interference signal and the second interferencesignal comprises calculating a first signal phase of the firstinterference signal and a second signal phase of the second interferencesignal.